Let n≥2 be an integer and let f be a 4n-variable polynomial with real coefficients. Assume that, for any 2n points (x1,y1),…,(x2n,y2n) in the Cartesian plane, f(x1,y1,…,x2n,y2n)=0 if and only if the points form the vertices of a regular 2n-gon in some order, or are all equal. Determine the smallest possible degree of f.(Note, for example, that the degree of the polynomial g(x,y)=4x3y4+yx+x−2 is 7 because 7=3+4.)Ankan Bhattacharya algebrapolynomialanalytic geometryRMM 2023